Question

Solve the system of equations:
y = 2x - 4
y= x^2 - 4

Answer 1

Answer:

correct question

$\\ \longmapsto$ y=2x -4

$\\ \longmapsto$y=x²-4

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The two intersections would be (3, 10) and (-2, 0)

Step-by-step explanation:

To solve this system of equations, set the two equations equal to each other and solve for x.

$\\ \mapsto$2x + 4 = x² + x - 2

$\\ \mapsto$2x = x² + x - 6

$\\ \mapsto$0 = x² - x - 6

$\\ \mapsto$0 = (x - 3)(x + 2)

Now set the parenthesis equal to zero to get the x values.

$\\ \mapsto$x - 3 = 0

$\\ \mapsto$x = 3

$\\ \mapsto$x + 2 = 0

$\\ \longmapsto$x = -2

Now we know the x values of each interception. We can find the y values by plugging into either equation.

$\\ \mapsto$y = 2x + 4

$\\ \mapsto$y = 2(3) + 4

$\\ \mapsto$y = 6 + 4

$\\ \longmapsto$y = 10

$\\ \mapsto$y = 2x + 4

$\\ \mapsto$y = 2(-2) + 4

$\\ \mapsto$y = -4 + 4

$\\ \longmapsto$y = 0